Question: What do the following two equations represent? $x+4y = 1$ $-x-4y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $x+4y = 1$ $4y = -x+1$ $y = -\dfrac{1}{4}x + \dfrac{1}{4}$ Putting the second equation in $y = mx + b$ form gives: $-x-4y = 2$ $-4y = x+2$ $y = -\dfrac{1}{4}x - \dfrac{1}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.